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help with automatic schedual planing

Hey Everyone, i hope someone can help me with this project and point me to the best way of solving it. I am new to programming. I am from with an automatic schedial planner for my compagny.
i tought i want to do it with Php and Mysql since it is the easy way for me to do it. so :
we have 10 employes, and every day we need 1 for the dayshift ( 6 hours ) and 2 for a management shift ( 6 hours ) and 1 for the night shift ( 17 hours ). all employes should work aproximatly 37 hours a week, and the schedual is rotating. and finally the workers can submit up to 5 requests a month ( fri days / courses ect )
i was thinking about doing a backtrack algorithm to associate the shift to the workers, is it the best way to do it ? to wich extend can i make an optimal plan fully automated ? and where should i start ? ( i was thinking about making tables for vailiability for each worker ? )